I would like a better sound in my system: Currently volume on speakers turned up to max, music and Youtube videos are not audible across the room. Switching to Windows this volume level can be heard across the street, volume is far to loud for the home.

Not certain what sound card to purchase and install in this desktop, for sound to perform at an acceptable level, and turn off the on board sound card 0: Generic [HD-Audio Generic]. Switching to card 1: Generic_1 [HD-Audio Generic], device 0: ALC662 rev3 Analog [ALC662 rev3 Analog] produces no sound.

From your screen shot, it doesn't look like Audio Mixer is showing your sound card. Instead of "HD Audio Generic (Alsa mixer)" I would expect to see "Advanced Micro Devices [AMD] FCH Azalia Controller". However, it looks like more selections are available from a drop-down menu. Do you have two sound cards by chance?